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Metamath Proof Explorer

Theorem rexpssxrxp

Description: The Cartesian product of standard reals are a subset of the Cartesian product of extended reals. (Contributed by David A. Wheeler, 8-Dec-2018)

		Ref	Expression
	Assertion	rexpssxrxp	⊢ ( ℝ × ℝ ) ⊆ ( ℝ^* × ℝ^* )

Proof

Step	Hyp	Ref	Expression
1		ressxr	⊢ ℝ ⊆ ℝ^*
2		xpss12	⊢ ( ( ℝ ⊆ ℝ^* ∧ ℝ ⊆ ℝ^* ) → ( ℝ × ℝ ) ⊆ ( ℝ^* × ℝ^* ) )
3	1 1 2	mp2an	⊢ ( ℝ × ℝ ) ⊆ ( ℝ^* × ℝ^* )